Question

$\frac{1}{log_{\sqrt{bc}}abc}+\frac{1}{log_{\sqrt{ca}}abc}+\frac{1}{log_{\sqrt{ab}}abc}$ has the value equal to-

• A. 1/2
• B. 1
• C. 2
• D. 4

Answer 1

Answer: (B)

1

Answer 2

Using the property $\frac{1}{\log_x y} = \log_y x$, the expression becomes: $\log_{abc}(\sqrt{bc}) + \log_{abc}(\sqrt{ca}) + \log_{abc}(\sqrt{ab})$ Using the property $\log_b x + \log_b y + \log_b z = \log_b (xyz)$: $\log_{abc}(\sqrt{bc} \cdot \sqrt{ca} \cdot \sqrt{ab}) = \log_{abc}(\sqrt{a^2 b^2 c^2}) = \log_{abc}(abc)$ Using the property $\log_b b = 1$: $\log_{abc}(abc) = 1$